Coupled Hydro-Mechanical Modelling of Gas Migration in Saturated Bentonite

Abstract

Bentonite is regarded as an ideal geomaterial for the engineering barrier system of a deep geological repository (DGR) where nuclear wastes are disposed, as it has several desirable properties for sealing the nuclear wastes, including low permeability, low diffusion coefficient, high adsorption capacity and proper swelling ability. Nevertheless, gas migration in saturated bentonite may undermine the sealing ability of the geomaterial. Previous experimental studies showed that the gas migration process is accompanied by complex hydromechanical (HM) behaviors, such as gas breakthrough phenomenon, development of preferential pathways, build-up of water pressure and total stress, nearly saturated state after gas injection test, localized consolidation, water exchange between clay matrix and developed fractures and self-sealing process. These experimentally observed behaviors should be properly modelled for conducting a reliable performance assessment for the geomaterial over the lifespan of DGR. In this thesis, two different coupled HM frameworks, i.e., one based on double porosity (DP) concept, referred to as coupled HM-DP framework, and the other on phase field (PF) method, referred to as coupled HM-PF framework, are proposed to simulate the gas migration process in saturated bentonite. For the coupled HM-DP framework, the saturated bentonite is assumed as a superposition of a MAcro-Continuum (MAC) and a MIcro-Continuum (MIC). Two-phase flow is only allowed in the MAC, whereas the MIC is impermeable to both water and gas. Nevertheless, the water can transfer between the MIC and the MAC under the water pressure gap. The first coupled HM model in this framework is based on a double effective stress concept. Mechanical behaviors of the MAC and the MIC are respectively governed by Bishop-type effective stress and Terzaghi’s effective stress. The model can well simulate the evolutions of both gas pressure and gas outflow rate, the water exchange between clay matrix and developed pathways, the high degree of saturation and the consolidation of clay matrix. To account for the development of preferential pathways, the damaging effect has been introduced in the framework. In this improved model, Bishop-type effective stress for the MAC is replaced by the independent stress state variables, i.e., net normal stress and suction, since using the net normal stress is beneficial to simulating tensile failure under high gas pressure. Numerical results showed that the damage-enhanced model can well describe the effect of the development of preferential pathways on the build-up of water pressure and total stress. In addition, the proposed hysteretic models for intrinsic and relative permeabilities make the coupled HM framework more flexible to reproduce the experimental results. To explicitly simulate the development of preferential pathways, a coupled HM-PF framework is developed by using Coussy’s thermodynamic theory and the microforce balance law. The coupled HM-PF framework is implemented in the standard Finite Element Method (FEM). To avoid the pore pressure oscillation and enhance the computational efficiency, a stabilized mixed finite element, in which linear shape functions are selected for interpolating all primary variables, is adopted to discretize the whole domain. In the developed framework, swelling pressure (initial stress) is accounted for by introducing a modified strain tensor that is the sum of the strain tensor due to deformation and the strain tensor calculated from the initial stress. The numerical results showed that the developed coupled HM-PF framework can capture some important behaviors, such as the discrete pathways, localized gas flow, built-up of water pressure and total stress under constant volume condition and nearly saturated state in clay matrix. A spatially autocorrelated random field is introduced into the framework to describe the heterogeneous distribution of HM properties in bentonite. The heterogeneity is beneficial to simulating the fracture branching and the complex fracture trajectory. Numerical results showed that some factors, such as Gaussian random field, coefficient of variation, boundary condition and injection rate, have significant influences on the fracture trajectory. At the end of the thesis, the obtained numerical results are synthesized and analyzed. Based on the analysis, the pros and cons of the developed numerical models are discussed. Corresponding to the limitations, some recommendations are proposed for future studies.